KOH + Zn + Ca(NO3)2 = H2O + NH3 + Ca(OH)2 + K2ZnO2

KOH potassium hydroxide + Zn zinc + Ca(NO_3)_2 calcium nitrate ⟶ H_2O water + NH_3 ammonia + Ca(OH)_2 calcium hydroxide + K2ZnO2

Balance the chemical equation algebraically: KOH + Zn + Ca(NO_3)_2 ⟶ H_2O + NH_3 + Ca(OH)_2 + K2ZnO2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 Zn + c_3 Ca(NO_3)_2 ⟶ c_4 H_2O + c_5 NH_3 + c_6 Ca(OH)_2 + c_7 K2ZnO2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Zn, Ca and N: H: | c_1 = 2 c_4 + 3 c_5 + 2 c_6 K: | c_1 = 2 c_7 O: | c_1 + 6 c_3 = c_4 + 2 c_6 + 2 c_7 Zn: | c_2 = c_7 Ca: | c_3 = c_6 N: | 2 c_3 = c_5 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 16 c_2 = 8 c_3 = 1 c_4 = 4 c_5 = 2 c_6 = 1 c_7 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 KOH + 8 Zn + Ca(NO_3)_2 ⟶ 4 H_2O + 2 NH_3 + Ca(OH)_2 + 8 K2ZnO2

+ + ⟶ + + + K2ZnO2

potassium hydroxide + zinc + calcium nitrate ⟶ water + ammonia + calcium hydroxide + K2ZnO2

Construct the equilibrium constant, K, expression for: KOH + Zn + Ca(NO_3)_2 ⟶ H_2O + NH_3 + Ca(OH)_2 + K2ZnO2 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: 16 KOH + 8 Zn + Ca(NO_3)_2 ⟶ 4 H_2O + 2 NH_3 + Ca(OH)_2 + 8 K2ZnO2 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i KOH | 16 | -16 Zn | 8 | -8 Ca(NO_3)_2 | 1 | -1 H_2O | 4 | 4 NH_3 | 2 | 2 Ca(OH)_2 | 1 | 1 K2ZnO2 | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 16 | -16 | ([KOH])^(-16) Zn | 8 | -8 | ([Zn])^(-8) Ca(NO_3)_2 | 1 | -1 | ([Ca(NO3)2])^(-1) H_2O | 4 | 4 | ([H2O])^4 NH_3 | 2 | 2 | ([NH3])^2 Ca(OH)_2 | 1 | 1 | [Ca(OH)2] K2ZnO2 | 8 | 8 | ([K2ZnO2])^8 The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([KOH])^(-16) ([Zn])^(-8) ([Ca(NO3)2])^(-1) ([H2O])^4 ([NH3])^2 [Ca(OH)2] ([K2ZnO2])^8 = (([H2O])^4 ([NH3])^2 [Ca(OH)2] ([K2ZnO2])^8)/(([KOH])^16 ([Zn])^8 [Ca(NO3)2])

Construct the rate of reaction expression for: KOH + Zn + Ca(NO_3)_2 ⟶ H_2O + NH_3 + Ca(OH)_2 + K2ZnO2 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: 16 KOH + 8 Zn + Ca(NO_3)_2 ⟶ 4 H_2O + 2 NH_3 + Ca(OH)_2 + 8 K2ZnO2 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i KOH | 16 | -16 Zn | 8 | -8 Ca(NO_3)_2 | 1 | -1 H_2O | 4 | 4 NH_3 | 2 | 2 Ca(OH)_2 | 1 | 1 K2ZnO2 | 8 | 8 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term KOH | 16 | -16 | -1/16 (Δ[KOH])/(Δt) Zn | 8 | -8 | -1/8 (Δ[Zn])/(Δt) Ca(NO_3)_2 | 1 | -1 | -(Δ[Ca(NO3)2])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) NH_3 | 2 | 2 | 1/2 (Δ[NH3])/(Δt) Ca(OH)_2 | 1 | 1 | (Δ[Ca(OH)2])/(Δt) K2ZnO2 | 8 | 8 | 1/8 (Δ[K2ZnO2])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -1/16 (Δ[KOH])/(Δt) = -1/8 (Δ[Zn])/(Δt) = -(Δ[Ca(NO3)2])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[NH3])/(Δt) = (Δ[Ca(OH)2])/(Δt) = 1/8 (Δ[K2ZnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | zinc | calcium nitrate | water | ammonia | calcium hydroxide | K2ZnO2 formula | KOH | Zn | Ca(NO_3)_2 | H_2O | NH_3 | Ca(OH)_2 | K2ZnO2 Hill formula | HKO | Zn | CaN_2O_6 | H_2O | H_3N | CaH_2O_2 | K2O2Zn name | potassium hydroxide | zinc | calcium nitrate | water | ammonia | calcium hydroxide | IUPAC name | potassium hydroxide | zinc | calcium dinitrate | water | ammonia | calcium dihydroxide |

| potassium hydroxide | zinc | calcium nitrate | water | ammonia | calcium hydroxide | K2ZnO2 molar mass | 56.105 g/mol | 65.38 g/mol | 164.09 g/mol | 18.015 g/mol | 17.031 g/mol | 74.092 g/mol | 175.6 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) | melting point | 406 °C | 420 °C | 562 °C | 0 °C | -77.73 °C | 550 °C | boiling point | 1327 °C | 907 °C | | 99.9839 °C | -33.33 °C | | density | 2.044 g/cm^3 | 7.14 g/cm^3 | 2.5 g/cm^3 | 1 g/cm^3 | 6.96×10^-4 g/cm^3 (at 25 °C) | 2.24 g/cm^3 | solubility in water | soluble | insoluble | soluble | | | slightly soluble | surface tension | | | | 0.0728 N/m | 0.0234 N/m | | dynamic viscosity | 0.001 Pa s (at 550 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | 1.009×10^-5 Pa s (at 25 °C) | | odor | | odorless | | odorless | | odorless |